\def\g{{\frak g}}
\def\C{{\Bbb C}}
We give branching formulas from so$(7,\C)$ to $\g_2$
for parabolic Verma modules attached to $\g_2$-compatible
parabolic subalgebras of so$(7,\C)$, and branching formulas
from $\g_2$ to sl$(3,\C)$ for parabolic Verma modules attached
to sl$(3,\C)$-compatible parabolic subalgebras of $\g_2$
respectively, under some assumptions on the parameters of
parabolic Verma modules.